LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zrzt01()

double precision function zrzt01 ( integer  M,
integer  N,
complex*16, dimension( lda, * )  A,
complex*16, dimension( lda, * )  AF,
integer  LDA,
complex*16, dimension( * )  TAU,
complex*16, dimension( lwork )  WORK,
integer  LWORK 
)

ZRZT01

Purpose:
 ZRZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with ZTZRZF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrices A and AF.
[in]N
          N is INTEGER
          The number of columns of the matrices A and AF.
[in]A
          A is COMPLEX*16 array, dimension (LDA,N)
          The original upper trapezoidal M by N matrix A.
[in]AF
          AF is COMPLEX*16 array, dimension (LDA,N)
          The output of ZTZRZF for input matrix A.
          The lower triangle is not referenced.
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A and AF.
[in]TAU
          TAU is COMPLEX*16 array, dimension (M)
          Details of the  Householder transformations as returned by
          ZTZRZF.
[out]WORK
          WORK is COMPLEX*16 array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK >= m*n + m.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 96 of file zrzt01.f.

98 *
99 * -- LAPACK test routine --
100 * -- LAPACK is a software package provided by Univ. of Tennessee, --
101 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
102 *
103 * .. Scalar Arguments ..
104  INTEGER LDA, LWORK, M, N
105 * ..
106 * .. Array Arguments ..
107  COMPLEX*16 A( LDA, * ), AF( LDA, * ), TAU( * ),
108  $ WORK( LWORK )
109 * ..
110 *
111 * =====================================================================
112 *
113 * .. Parameters ..
114  DOUBLE PRECISION ZERO, ONE
115  parameter( zero = 0.0d0, one = 1.0d0 )
116 * ..
117 * .. Local Scalars ..
118  INTEGER I, INFO, J
119  DOUBLE PRECISION NORMA
120 * ..
121 * .. Local Arrays ..
122  DOUBLE PRECISION RWORK( 1 )
123 * ..
124 * .. External Functions ..
125  DOUBLE PRECISION DLAMCH, ZLANGE
126  EXTERNAL dlamch, zlange
127 * ..
128 * .. External Subroutines ..
129  EXTERNAL xerbla, zaxpy, zlaset, zunmrz
130 * ..
131 * .. Intrinsic Functions ..
132  INTRINSIC dble, dcmplx, max
133 * ..
134 * .. Executable Statements ..
135 *
136  zrzt01 = zero
137 *
138  IF( lwork.LT.m*n+m ) THEN
139  CALL xerbla( 'ZRZT01', 8 )
140  RETURN
141  END IF
142 *
143 * Quick return if possible
144 *
145  IF( m.LE.0 .OR. n.LE.0 )
146  $ RETURN
147 *
148  norma = zlange( 'One-norm', m, n, a, lda, rwork )
149 *
150 * Copy upper triangle R
151 *
152  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), work,
153  $ m )
154  DO 20 j = 1, m
155  DO 10 i = 1, j
156  work( ( j-1 )*m+i ) = af( i, j )
157  10 CONTINUE
158  20 CONTINUE
159 *
160 * R = R * P(1) * ... *P(m)
161 *
162  CALL zunmrz( 'Right', 'No tranpose', m, n, m, n-m, af, lda, tau,
163  $ work, m, work( m*n+1 ), lwork-m*n, info )
164 *
165 * R = R - A
166 *
167  DO 30 i = 1, n
168  CALL zaxpy( m, dcmplx( -one ), a( 1, i ), 1,
169  $ work( ( i-1 )*m+1 ), 1 )
170  30 CONTINUE
171 *
172  zrzt01 = zlange( 'One-norm', m, n, work, m, rwork )
173 *
174  zrzt01 = zrzt01 / ( dlamch( 'Epsilon' )*dble( max( m, n ) ) )
175  IF( norma.NE.zero )
176  $ zrzt01 = zrzt01 / norma
177 *
178  RETURN
179 *
180 * End of ZRZT01
181 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
double precision function zrzt01(M, N, A, AF, LDA, TAU, WORK, LWORK)
ZRZT01
Definition: zrzt01.f:98
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zunmrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMRZ
Definition: zunmrz.f:187
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